We introduce a criterion for a set to be Γ-null. Using it we give a shorter proof of the result that the set of points where a continuous convex function on a separable Asplund space is not Fréchet differentiable is Γ-null. Our criterion also implies a new result about Gâteaux (and Hadamard) differentiability of quasiconvex functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-5,
author = {Jaroslav Ti\v ser and Lud\v ek Zaj\'\i \v cek},
title = {A criterion of $\Gamma$-nullness and differentiability of convex and quasiconvex functions},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {149-164},
zbl = {1339.46044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-5}
}
Jaroslav Tišer; Luděk Zajíček. A criterion of Γ-nullness and differentiability of convex and quasiconvex functions. Studia Mathematica, Tome 231 (2015) pp. 149-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-5/